Predicting the Effect of Fission Products in UO

2 Presentation at the VERCORS meeting Kaajal H. Desai a , David Parfitt a , Scott L. Owens b , Robin W. Grimes a a Department of Materials, Imperial College, Prince Consort Road, London, UK b Nexia Solutions, Hinton House, Risley, Warrington, Chesire UK Imperial College OF SCIENCE, TECHNOLOGY AND MEDICINE

Aim:

demonstrate what atomic scale computer simulation developing can a provide, better that is useful understanding of for the behaviour of nuclear fuels (particularly as they relate to fission product behaviour).

What can simulations do for you?

• Correlate experimental data with existing physical models (fill in the gaps and work out what’s missing).

• Generate data for known physical processes (point the way to better hunting grounds for experimental work).

• Develop new physical models that underpin phenomena (work out what science actually matters).

First – Correlate experimental data with physical models

• Use fission product inventories to investigate fuel swelling.

• Lattice swelling/contraction due to accommodation of soluble fission products as a function of fission product concentration.

• Affect on mechanical properties – elastic constants and bulk moduli as a function of fission product concentration.

First – Correlate experimental data with physical models

• The Physical process is well established.

• No new “science” is being suggested.

• Checking existing data and correlating it.

• Hence: fillng in the gaps and working out what’s missing.

Swelling Calculation

  Defect volume,

V D

, is calculated by:

K T V 0

(Å 3

V D

 

K

(Å 3 ) initial unit cell volume

T V

0

df dV



T

eV -1 ) is the isothermal compressibility,

f

(eV) the internal defect formation energy calculated within the Mott-Littleton approximation Mechanical constants are calculated using:

K T

 

c

11  3 2

c

12   Bulk Modulus

B

 1

K T

  

Model Considerations

Range of Fission Products (FP) Different solution sites – U and O substitution, interstitial octahedral site, cluster sites Fuel Stoichiometry   Zr 4+ , Ce 4+ - sites: ,

U Ce U X

Sr 2+ - sites : Isolated Clustered

Sr U

''

U

 

V

 2

U O



U

 

Sr U

'' 

Sr U

'' : :

V O

  

U U



X

'  

U



U



Sr U

'' : 2

U U

 

X

 Y 3+ , La 3+ , Pr 3+ , Nd 3+ , Sm 3+ , Eu 3+ , Gd 3+ , Dy 3+ 2

La

'

U



V



O



La

'

U



U



U



La U

' 

La U

' : :

V O



U



U

 

X

  

La U

'  2

La U

' sites: :

V O

  

X

Results I: Zr accommodation

Results II: Ce accommodation

FP Accommodation: Sr

   Number of ways Sr can be accommodated in lattice UO 2 - substitution on U site is energetically favoured Charge compensated in 2 ways V O ·· Oxygen vacancy formation Uranium oxidation, U 5+ U U · formation  Similarly for the trivalent, Y and lanthanide fission products

Results III: Sr accommodation

Results IV: La accommodation

Results V: Pr accommodation

Results VI: Nd accommodation

Results VII: Sm accommodation

Results VIII: Eu accommodation

Results IX: Gd accommodation

Results X: Dy accommodation

Results XI: Predicted Change in Bulk Modulus due to Sr

Results XIII: Predicted Change in Bulk Modulus due to Zr and Ce

Summary

 A specific burnup yields a specific fission product inventory. This work aims to provide data from which it is possible to determine a change of lattice parameter or change in mechanical property of the UO 2 lattice as a consequence of the dissolved fraction of those fission products.  For example,  Sr 2+ --> Increased lattice parameter  Zr 4+ --> Decreased lattice parameter

Second – Generate data for known physical processes

• The aim is to help to direct experimental work.

• The physical process is well established, but the significance to fuels not necessarily realised.

• Appropriate experimental data does not yet exist.

• Classic example: compositional changes due to segregation.

Aim of Segregation Study

•

Computer simulation is used to investigate the accommodation and segregation of fission products to the (111), (110) and (100) surfaces of UO 2  Fission products considered: Ce 4+ , Zr 4+ , Ba 2+ , Sr 2+ , Kr 0 and Xe 0  Ba 2+ vacancy and Sr 2+  Kr 0 and Xe 0 are charge compensated by a single oxygen are compensated by two oxygen vacancies • Important results concern:  Segregation dependence on the surface type   Defect cluster orientation with respect to a given surface Anion termination configuration for dipolar surfaces • This work provides information regarding the anisotropic release of fission products.

Methodology

• Computational codes CASCADE and MARVIN are used.

• A defect (isolated or clustered) is introduced to a characteristic lattice and moved stepwise through the bulk.

• The total energy of Region 1 is calculated for each step and the energies are compared with respect to when the cluster is furthest from the surface (i.e. in the bulk).

Divalent ClusterConfigurations: (111) • The nearest neighbour {(Ba/Sr U )’’:(V O ) ..

} configuration is preferred.

• There are four unique nearest neighbour cluster configurations with respect to the (111) surface, shown below.

• Each of these configurations must be modelled.

Ce 4+ and Zr 4+ (111) Segregation • The Zr 4+ segregation energy, E S = 0.26eV, the trap energy, E T = 0.35eV, which suggests that Zr 4+ remain trapped just beneath the (111) surface.

• For Ce 4+ , E S = 0.23eV, which suggests that Ce 4+ does not segregate to the (111) surface.

• (E T - E S ) is negligible, which suggests that the trapping observed with Zr 4+ is not present.

Ba 2+ and Sr 2+ (111) Segregation • The segregation energy E S 2.71eV for Ba 2+ , thus Ba 2+ = will segregate to the (111) surface.

• A similar trend is observed for Sr 2+ , where E S = -1.60eV, though the driving force is reduced.

• In the bulk (  10 Å) there is little cluster configuration preference.

• Near to the surface, there is a dependence on defect cluster configuration.

Ce 4+ and Zr 4+ (110) Segregation • The Zr 4+ segregation energy, E S Zr 4+ = 0.14eV, which suggests that will not segregate to the (110) surface.

• The nonlinear change in energy is due to alternating compression and dilation of atomic layers.

• For Ce 4+ E S suggests that = 0.67eV which Ce 4+ does not segregate to the (110) surface, more strongly than Zr 4+ .

• The trend for Ce 4+ and Zr 4+ not segregating to the (110) surface is similar to the trend observed for the (111).

Ba 2+ and Sr 2+ (110) Segregation • The Ba 2+ , segregation energy, E S = -2.84eV, suggests that Ba segregate to the (110) surface.

2+ will • A similar trend is observed for Sr 2+ where E S = -1.67eV; clearly the driving force is reduced.

• The segregation of Ba 2+ and Sr 2+ is very similar to that observed with the (111); similar segregation energies and cluster dependence nearer to the surface.

Conclusions Concerning Segregation • Computer simulation calculations suggest that Ce 4+ and Zr 4+ show no tendency to segregate to the (111) or (110) surfaces of UO 2 .

• Zr 4+ demonstrates a tendency to segregate to the (100)A surface, which suggests segregation is a function of surface.

• Ba 2+ and Sr 2+ display a tendency to segregate to the (111) and (110) surfaces, with cluster configuration becoming important near the surface in both cases.

• Segregation is not only a function of fission product chemistry and surface, but also cluster configuration with respect to surface and anion termination in the case of Type 3 surfaces.

• Fission product release will be highly anisotropic.

Third – identify new physical processes

Aims of the study

 Develop a robust computational model that can simulate UO 2 and fission gasses. It must replicate:  High temperature behaviour and defect energies  Good core-core repulsion for high energy collisions  Apply this model to predict the evolution of bubbles with respect to:  Bubble size  Fission gas pressure  Temperature of material  Recoil energy

All micrographs courtesy of Ian Ray ITU Transgranular fracture showing aligned metal particles leading to a grain boundary Transgranular fracture showing internal void, smaller gas bubbles and larger bubbles at grain boundaries

Intergranular and Transgranular Fracture

Molecular dynamics of radiation enhanced helium re-solution

Helium in bubbles can return to the crystal lattice via radiation-enhanced re-solution rather than thermal resolution ...

But how does this actually work in practice?

It is thought that high-energy fission fragments 'knock out' helium atoms from bubbles leading to resolution.

What Bubbles?

 Several different bubble sizes and shapes have been investigated:  Octahedra constructed from (111) surfaces  Infinite pores from (110) surfaces  Spheres  Larger 'infinite' slab surfaces  In UO 2 the morphology of the bubbles is roughly spherical but (111) surfaces are observed (which also dominate equilibrium voids).

MD Simulation of 5 keV U <111> Recoil

Event sequence:

• Ballistic phase.

• Thermal spike.

• Displacement damage interacts with the He bubble disrupting the bubble/lattice interface.

• Beginning of recovery phase.

MD Simulation of 5 keV U <111> Recoil

Event sequence:

• Ballistic phase and thermal spike are not seen.

• Displaced lattice ions interacts with the He bubble disrupting the bubble/lattice interface.

• He “leaks” into the damaged (partly disordered) lattice.

MD Simulation of 5 keV U <111> Recoil

Event sequence:

• Ballistic phase.

• Thermal spike.

• Lattice ions are displaced into the bubble.

• UO 2 units are relocated across the bubble facilitating the overall movement of the bubble.

Why is this exciting?

• Physics behind this mode of radiation enhanced resolution is fundamentally different to what has been proposed previously.

• May explain some 'anomalous' terms in bubble migration models.

• More accurate and confident modelling leads to less conservatism in fuel performance codes.

Directions of Further Work

• • • • Long timescale dynamics of bubble migration.

He migration along dislocations.

'Phase diagram' of the bubbles as a function of temperature, He pressure and displacement cascade energy.

Examine Xe gas behaviour as well – Xe adopts solid structures in fission gas bubbles. • Aim to aid in reducing conservatism.

Summary

Imperial College OF SCIENCE, TECHNOLOGY AND MEDICINE • A simple computational model has been used to generate structure (and defect structure) property composition relationships.

• Correlated experimental data with physical models (filled in some gaps and work out what’s missing).

• Identified computational variations close to surfaces (pointed the way for experimental investigations).

• Developed new physical models that underpin phenomena (worked out what bit actually matters).

• Need to use a range of computational techniques to underpin and generate the defect property relationships.